Frank Williams talks so softly, and with such biting honesty and humour, that it feels imperative to sit so close to him that his hands involuntarily brush mine when he becomes animated. Before Sunday's British Grand Prix, with his first involvement in the race occurring in 1969, Williams raises an amused eyebrow in his wheelchair. His cars have started, he suggests, 43 previous British grands prix.

"It's something like that," he says, scrunching up his face in disdain at the passing years. There is so much clatter around us while we sit in his team's bustling motorhome that I'm compelled to hold a tiny recorder right under the mouth of an amusing and gently acerbic man. Williams does not seem to mind the enforced intimacy and he reacts with winning candour – even when confronted by a banal question.

Asked if he is optimistic about his team's prospects at Silverstone, especially in the wake of their first grand prix victory in eight years, Williams offers a crinkly smile. "I'm never that optimistic because life is cruel. Just when you think, 'woaah, you've got to watch this!' it all goes wrong. If you're an athlete you are in control of yourself and your fate is down to you. But, in Formula One, we have so many links in the chain and you only need one link to go wrong. There's always a lot to worry about."

Williams has suffered life's cruelties in graphic ways. The death of his first driver, Piers Courage, at the Dutch Grand Prix in 1970 marked him for life – and yet the loss of Ayrton Senna, 24 years later, proved still more haunting. And between those tragedies, in March 1986, Williams sustained the spinal-cord injury that paralysed him, in a car accident. Yet, as Ron Dennis, his former counterpart at McLaren, famously remarked, Williams became still more dangerous to his opponents. As a quadriplegic, Williams had more time to think and plot the supremacy of a team that won nine constructors' titles and seven drivers' championships between 1980 and 1997.

That sustained success has made the past decade hard to bear. It is startling to be reminded that, before victory this May in Barcelona, 132 races had passed without a win for Williams. And yet this quintessential British team has retained an almost unprecedented popularity within the usually bitter paddock. There was genuine delight that Williams had won again when Pastor Maldonado took the chequered flag at the Spanish Grand Prix. "I was aware of it," Williams says of that warm affection, "but I never take it for granted." The 70-year-old racing man looks up from his stationary place and his eyes sparkle. "You know," he murmurs, "someone once said that assumption is the mother of all fuck-ups. It's a great line, but it's also true. It sums up Formula One. You can take nothing for granted. Maybe if you're Red Bull or McLaren you can say, on a Saturday night: 'Well, we should have at least one car in the top three tomorrow.' But even then you cannot be entirely sure. I learnt that years ago."

When Maldonado crossed the line in Barcelona, and Williams had their first win since 2004, their team principal felt drained. "There was only relief," he says. "Relief that the car had won again after such a long time. And then came the worry that we keep it up and do it again. That's why there's been no complacency since then."

As has happened so often with Williams during his tumultuous life, the relief did not last. Just as he had finished talking to his jubilant team, who had gathered around his wheelchair in Barcelona, Williams noticed an ominous sign. "Smoke came billowing out of the back of the garage. It was a lot of black smoke and we had to move quickly." The fire that engulfed the Williams garage soon after Maldonado's unexpected triumph left 31 people in need of medical treatment. But there were no fatalities – and, fortunately, only one serious burns-related injury to a team member. As his recovery continues, so his boss has been able to reflect on the reasons for a return to form. "We've acquired several good people who have made a real difference," Williams explains.

Mike Coughlan, the new chief designer, had been suspended from Formula One after his involvement in the Spygate scandal while working for McLaren in 2007. Over the past 14 months, Coughlan has set about restoring his reputation. Mark Gillan, chief operations engineer since last September, has also improved communication between the factory and the team. "The company is now in good hands, with Mike leading the design and Mark in charge of racing operations," Williams says. "They're helping us regain our momentum."

Williams have also benefited from two mature men – if still relatively inexperienced F1 drivers – in Maldonado and Bruno Senna. "Pastor is a character in his quiet way. He can seem happy-go-lucky, but he spends a lot of time with the engineers and he's deeply sincere and devoted to racing. All the mechanics communicate well with him and he's a major contributor [to Williams' resurgence]. He's 27 and maturity is very important."

Senna, at 28, has had to overcome the burden of his near-mythic name and memories of his uncle's imperious ability. "It's not because he has the same name or even the same talent as Ayrton," Williams says of Bruno, who has scored 16 points to Maldonado's 29 this season. "Bruno was just a good candidate and a very intelligent person. There were no negatives – just some good, positive reasons to say: 'Yes, let's give him a go.'"

His uncle, however, remains Williams' favourite driver. The poignance of that choice is accentuated by the fact Ayrton Senna, a three-times world champion and one of the greatest racers who ever lived, died in only his third race in a Williams car. At the San Marino Grand Prix, on 1 May 1994, Senna's car suffered a suspected steering-column failure. Williams and his chief engineer, the exemplary Adrian Newey, were later charged with manslaughter. The allegations were eventually quashed, but the impact of Senna's death can still be seen on Williams's face.

"Ayrton Senna was a great man," he says. "He was public property and immensely popular. It was just a very sad day for millions of people. I was very emotional about it because it was one of our cars and he was such a special person. He was immensely charming, but also tough, ruthless and brilliantly gifted. And it just destroyed him."

At the outset of his career, in the early 1970s, Williams was reduced to carrying out a chunk of his F1 business while using a public telephone booth. "There was a bit of that," he cackles, "because in the old days we didn't have television coverage or the revenue that brings. It was very hard work and hand-to-mouth stuff."

In 1977, Williams and his chief engineer, Patrick Head, took over an empty carpet warehouse in Didcot and transformed their struggling team. Describing Head as "a complete guiding light", Williams suggests his old ally still assists him, despite his retirement last year. "Patrick can say, 'if I were you I'd do it like this rather than like that'."

Williams himself is no longer a board member of his own company. His daughter, Claire, has replaced him, but he remains the team principal. "I'd rather not be reminded that I'm 70. But I am. On the other hand, I'm too busy to worry about it."

In a similar vein, his wife, Ginny, who sits at his side just before our interview, remembers that when Williams was paralysed he stared up at her from his hospital bed. He told her he'd had 43 years of a fantastic life – and he would look forward to another 40-odd years of a different life. "I said something like that," Williams nods, before almost snorting at himself. "I meant it at the time, but I soon changed my mind."

That self-deprecation cannot mask his consuming desire to compete in the brutal business of Formula One. "I'm at work every day of the week because there is a lot to do and I love F1. I'm just not ready to make a dramatic change in my life – like staying at home."

The British Grand Prix, which Williams has won 10 times, is always an emotion-packed race for him, especially because it marked his first victory. "I found it overwhelming," he says of Clay Regazzoni's win in 1979. "I'm not an emotional person, but it was an unforgettable experience. It was truly heartwarming and, even if I say it myself, a popular win. It really was a turning point for Williams."

Maldonado's win in Barcelona might be another turning point. As the past merges with the present, and Williams compares drivers then and now, there is a familiar slice of good-natured cheek in him. "Ayrton Senna," he says again when asked to name the best driver he has ever seen. "Alan Jones [who won Williams's first drivers' championship in 1980] was also special. He was a very funny guy. Tough but immensely skilled. He won the championship and then he just pissed around. He could have won again and again. He was that good. But he was the kind of person who said, 'been there, done that'.

"Today, [Sebastian] Vettel is very good. And Lewis [Hamilton]. If you said to me that all the drivers today are free and they're all desperate to get into Williams, I would say: 'Send in Lewis.' I'd say that because he's English and a winner. Lewis? I'd take him any time!"

Hamilton, of course, was among the many who entered the Williams garage to offer his congratulations in Barcelona. The old knight of the track nods at the reminder – but his eyes glitter more with a devilish desire to attract drivers of Hamilton's calibre again. "What we need is a faster racing car," Williams says. "That does not necessarily come from a big bank balance – but from a real brain-box. We're certainly getting there now."

• This article was amended on 8 July 2012. The original said the "S", a tribute to Ayrton Senna, had been taken off the Williams car. This is incorrect and the "S" remains.